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4 years ago

Given the figure. Find AC.

Mathematics

1 answer:

Angelina_Jolie [31]4 years ago

7 0

Image is missing, so i have attached it.

Answer:

AC = 10sin 40°

Step-by-step explanation:

From the diagram attached, using terms in trigonometric ratio, AC is the opposite side, BC is the adjacent side and AB is the hypotenuse.

Thus, since we want to find AC;

We know that in trigonometric ratios; opposite/hypotenuse = sin θ

In the diagram, θ = 40° and AB = 10

Thus,

AC/10 = sin 40°

Multiply both sides by 10 to get;

AC = 10sin 40°

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Which of the following is the least? A.0.105 B.0.501 c.o.015 D.0.15

SCORPION-xisa [38]

Is C 0.015? If so, then C, because if you imagine all of the numbers to the right as whole numbers, you get, in order from least to greatest, c, a, d, b. C is the answer.

8 0

4 years ago

If the length of the minute hand of the clock in London commonly known as "Big Ben" is 11.25' from the center of the clock to th

DochEvi [55]

Answer:

33.15 square inches.

Step-by-step explanation:

Given:

Length of the minute hand is 11.25' from the center of the clock to the tip of the hand.

Question asked:

What is the area swept out by the minute hand as it moves 5 minutes of time?

Solution:

As length of the minute hand is '11.25' from the center of the clock to the tip of the hand means radius of the circle, r = 11.25 inches.

First of all we will find area of circle swept by the minutes hand,

$Area\ of\ circle=\pi r^{2}$

$=\frac{22}{7} \times11.25\times11.25\\\\ =\frac{2784.375}{7} \\ \\ =397.77\ square\ inches$

When minute hand moves 60 minutes, it makes one circle of area 397.77 square inches.

By using unitary method, we will calculate area swept by minute hand in 5 minutes:-

In 60 minutes, area swept = 397.77 square inches

In 1 minute, area swept = $\frac{397.77}{60}$

In 5 minutes, area swept = $\frac{397.77}{60}\times5=\frac{1988.85}{60} =33.15\ square\ inches$

Thus, the area swept out by the minute hand is 33.15 square inches when it moves 5 minutes.

8 0

4 years ago

A recipe for sparkling grape juice calls for 1 1/2 quarts of sparkling water 3/4 quart of grape juice. Q1: How much sparkling wa

kogti [31]

Answer:

1) 18 Quart of Sparkling water need to mix with 9 quart grape juice

2) 15/2 Quart of grape juice required for 15/4 quarts of sparkling water.

3) Quantity of grape juice and sparkling water in 100 quart of punch are 33 1/3 quart and 66 2/3 quart respectively.

Step-by-step explanation:

1 1/2 quarts = 1 + (1/2) = 3/2 quarts

1) water required for 3/4 quart of grape juice = 3/2 quarts

so water required for 1 quart of grape juice = (3/2) ÷ (3/4) = (3/2)× (4/3) = 2 quarts

so water required for 9 quart of grape juice = 9 * 2 = 18 quart

18 Quart of Sparkling water need to mix with 9 quart grape juice

2) From solution of 1 ,

For 18 quart of Sparkling water , grape juice require = 9 quart

So for 1 quart of Sparkling water , grape juice require = 9÷18 = 1/2 Quart

so for 15/4 quart of Sparkling water , grape juice require = 1/2 × 15/4 =

15/2 Quart of grape juice required for 15/4 quarts of sparkling water.

in 1 we calculated that 18 Quart of Sparkling water need to mix with 9 quart grape juice that is 2 quart of Sparkling water need to mix with 1 quart of grape juice.

In other words 1 quart of grape juice + 2 quart of sparkling water is 3 quart of punch.

Quantity of Grape juice in 3 quart of punch = 1 quart

so quantity of grape juice in 1 quart of punch = 1/3 quart

And quantity of grape juice in 100 quart of punch = 100×(1/3) = 100/3 =

33 1/3

Quantity of sparkling water in 3 quart of punch = 2 quart

so quantity of sparkling water in 1 quart of punch = 2/3 quart

And quantity of sparkling water in 100 quart of punch = 100 ×2/3 quart = 66 2/3

3 0

4 years ago

Find the inverse of the given function. f(x) = 7x – 4

lukranit [14]

Hi there!

$\large\boxed{y = \frac{x + 4}{7}}$

f(x) = 7x - 4

Rewrite f(x) with y:

y = 7x - 4

Swap the x and y variables:

x = 7y - 4

Solve for y:

x + 4 = 7y

y = (x + 4)/7

3 0

3 years ago

Let p(x) be a polynomial of degree 10 such that p(k)=2^k for k=0,1,2,...,10.find p (11)

monitta

Answer:

p (11)=2^11

p (11)=2048

7 0

3 years ago