All categories

2 years ago

What is the measure of angle BDC?

Mathematics

1 answer:

serious [3.7K]2 years ago

7 0

Answer:

Like the angles BAC (56°) and BDC has the same arc BC in the circumference, these angles must be congruent, then angle BDC must be equal to 56°.

You might be interested in

A ball with mass m kg is thrown upward with initial velocity 28 m/s from the roof of a building 17 m high. Neglect air resistanc

Nutka1998 [239]

a. At its maximum height, the ball has zero vertical velocity, so

$-\left(28\dfrac{\rm m}{\rm s}\right)^2=2(-g)(y_{\rm max}-17\,\mathrm m)$

$\implies y_{\rm max}=57\,\mathrm m$

b. The ball's height in the air $y$ at time $t$ is given according to

$y=17\,\mathrm m+\left(28\dfrac{\rm m}{\rm s}\right)t-\dfrac g2t^2$

Solve for $t$ when $y=0$ :

$17+28t-4.9t^2=0\implies t\approx6.3\,\mathrm s$

3 0

2 years ago

Two brothers, Mark and Charles, each inherit $31000. Mark invests his inheritance in a savings account with an annual return of

Nutka1998 [239]

Answer:

$1,085

Step-by-step explanation:

Data provided in the question:

Amount inherited and invested i.e principle = $31,000

Annual return for Mark on savings account = 2.9% = 0.029

Annual return for Charles on CD = 6.4% = 0.064

Now,

The Interest earned by Mark in 1 year = principle × Rate × Time

= $31,000 × 0.029 × 1

= $899

The Interest earned by Charles in 1 year = principle × Rate × Time

= $31,000 × 0.064 × 1

= $1,984

Therefore,

More Money that Charles have than Mark = $1,984 - $899

= $1,085

7 0

3 years ago

Solve the right triangle for x.

dlinn [17]

Given:

The given figure is a right triangle.

The measure of one of the angle is 37°

One of the length of the legs of the triangle is 11 cm

The length of the hypotenuse is x.

We need to determine the value of x.

Value of x:

The value of x can be determined using the trigonometric ratio.

Thus, we have;

$cos \ \theta=\frac{adj}{hyp}$

Substituting the values, we have;

$cos \ 37^{\circ}=\frac{11}{x}$

Simplifying, we get;

$x=\frac{11}{cos \ 37^{\circ}}$

$x=\frac{11}{0.799}$

$x=13.767$

Rounding off to the nearest hundredth, we get;

$x=13.77$

Thus, the value of x is 13.77 cm.

3 0

3 years ago

Solve trigonometric function 2csc∅- 2cos^2 ∅ ×csc∅

Eduardwww [97]

Answer:

$2\sin(\theta)$

Step-by-step explanation:

$\csc(\theta)=\dfrac{1}{\sin(\theta)}$

$\sin^2(\theta)+\cos^2(\theta)=1\implies \sin^2(\theta)=1-\cos^2(\theta)$

$2\csc(\theta)- 2cos^2(\theta)\times csc(\theta)$

$=\dfrac{2}{\sin(\theta)}-\dfrac{ 2cos^2(\theta)}{\sin(\theta)}$

$=\dfrac{ 2[1-cos^2(\theta)]}{\sin(\theta)}$

$=\dfrac{ 2sin^2(\theta)}{\sin(\theta)}$

$=2\sin(\theta)$

6 0

2 years ago

Read 2 more answers

Perform the following calculations. In each case, first estimate the solution without using a calculator and then do the calcula

kakasveta [241]

Answer:

For a: The answer is $2.3\times 10^1$

For b: The answer is $8.0\times 10^{-6}$

For c: The answer is 127.6

For d: The answer is $4.66\times 10^4$

Step-by-step explanation:

Significant figures are defined as the figures in a number which express the value -the magnitude of a quantity to a specific degree of accuracy is known as significant digits.

Rules for significant figures:

Digits from 1 to 9 are always significant and have infinite number of significant figures.
All non-zero numbers are always significant. For example: 654, 6.54 and 65.4 all have three significant figures.
All zero’s between integers are always significant. For example: 5005, 5.005 and 50.05 all have four significant figures.
All zero’s preceding the first integers are never significant. For example: 0.0078 has two significant figures.
All zero’s after the decimal point are always significant. For example: 4.500, 45.00 and 450.0 all have four significant figures.
All zeroes used solely for spacing the decimal point are not significant. For example : 8000 has one significant figure.

Rule applied for the addition and subtraction is:

The least precise number present after the decimal point determines the number of significant figures in the answer.

Rule applied for the multiplication and division is:

The number of significant digits is taken from the value which has least precise significant digits.

For the given options:

Option a: (2.7)(8.632)

The given problem is a multiplication one.

$\Rightarrow (2.7\times 8.632)=23.3$

Here, the least precise significant digits are 2. So, the answer is $2.3\times 10^1$

Option b: (3.600 x 10^-4) / 45

The given problem is a division one.

$\Rightarrow \frac{(3.600\times 10^{-4})}{45}=0.08\times 10^{-4}$

Here, the least precise significant digits are 2. So, the answer is $8.0\times 10^{-6}$

Option c: 2.365 + 125.2

The given problem is an addition one.

$\Rightarrow (2.365+125.2)=127.565$

Here, the least precise significant digits after decimal is 1. So, the answer is 127.6

Option d: (4.753 x 10^4) - (9 x 10^2)

The given problem is a subtraction one.

$\Rightarrow (4.753\times 10^4)-(9\times 10^2)=(4.753\times 10^4)-(0.09\times 10^4)=4.663\times 10^4$

Here, the least precise significant digits after decimal are 2. So, the answer is $4.66\times 10^4$

3 0

3 years ago