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2 years ago

Can someone please help me and explain how to solve this question

Mathematics

1 answer:

Alex2 years ago

7 0

I see this triangle is isosceles. Thus, it has 2 sides of length 8 and 2 angles of measure 30 degrees.

(30 deg) + (30 deg) + (angle A) MUST add up to 180 degrees.

Thus, 60 deg + Angle A = 180 deg, so that Angle A = (180 - 60) deg, or 120 deg (answer)

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A juggler tosses a ball into the air . The balls height, h and time t seconds can be represented by the equation h(t)= -16t^2+40

malfutka [58]

PART A

The given equation is

$h(t) = - 16 {t}^{2} + 40t + 4$

In order to find the maximum height, we write the function in the vertex form.

We factor -16 out of the first two terms to get,

$h(t) = - 16 ({t}^{2} - \frac{5}{2} t) + 4$

We add and subtract

$- 16(- \frac{5}{4} )^{2}$

to get,

$h(t) = - 16 ({t}^{2} - \frac{5}{2} t) + - 16( - \frac{5}{4})^{2} - -16( - \frac{5}{4})^{2} + 4$

We again factor -16 out of the first two terms to get,

$h(t) = - 16 ({t}^{2} - \frac{5}{2} t + ( - \frac{5}{4})^{2} ) - -16( - \frac{5}{4})^{2} + 4$

This implies that,

$h(t) = - 16 ({t}^{2} - \frac{5}{2} t + ( - \frac{5}{4}) ^{2} ) + 16( \frac{25}{16}) + 4$

The quadratic trinomial above is a perfect square.

$h(t) = - 16 ( t- \frac{5}{4}) ^{2} +25+ 4$

This finally simplifies to,

$h(t) = - 16 ( t- \frac{5}{4}) ^{2} +29$

The vertex of this function is

$V( \frac{5}{4} ,29)$

The y-value of the vertex is the maximum value.

Therefore the maximum value is,

$29$

PART B

When the ball hits the ground,

$h(t) = 0$

This implies that,

$- 16 ( t- \frac{5}{4}) ^{2} +29 = 0$

We add -29 to both sides to get,

$- 16 ( t- \frac{5}{4}) ^{2} = - 29$

This implies that,

$( t- \frac{5}{4}) ^{2} = \frac{29}{16}$

$t- \frac{5}{4} = \pm \sqrt{ \frac{29}{16} }$

$t = \frac{5}{4} \pm \frac{ \sqrt{29} }{4}$

$t = \frac{ 5 + \sqrt{29} }{4} = 2.60$

or

$t = \frac{ 5 - \sqrt{29} }{4} = - 0.10$

Since time cannot be negative, we discard the negative value and pick,

$t = 2.60s$

8 0

3 years ago

Consider a t distribution with 7 degrees of freedom. Compute P(-1.29 < t < 1.29). Round your answer to at least three deci

marusya05 [52]

Answer:

Step-by-step explanation:

Given that there is a t distribution with 7 degrees of freedom.

P(-1.29 < t < 1.29)=1-0.2380

=0.7620

b) Now there is a different t distribution with 18 df.

When $P(t\leq c)=0.05$

c=-1.733

7 0

2 years ago

A 90-day simple interest loan in the amount of $2350 will be paid in full in the amount of $2500 . Find the rate of the loan.

ivolga24 [154]

Answer:

The rate of simple interest is 25.89 %

Step-by-step explanation:

Given as :

The principal = $2350

The Amount = $2500

The time period = 90 days = $\frac{90}{365}$ year = 0.2465 year

Let The rate of interest = R %

So, Interest = Amount - Principal

Or, Interest = $2500 - $2350 = $150

<u>From Simple Interest method </u>

Simple Interest = $\frac{Principal\times rate\times Time}{100}$

Or, $150 = $\frac{$2350\times rate\times 0.2465 }{100}$

or, $150 × 100 = $579.275 × Rate

So, Rate = $\frac{15000}{579.275}$

∴ Rate = 25.89 %

Hence The rate of simple interest is 25.89 % Answer

6 0

3 years ago

A cone has a slant height of a 26 cm and a radius of 10 cm what is the height of the cone

Vedmedyk [2.9K]

The height of the cone is 24 cm.

<h3>How is the slant height calculated?</h3>

The distance along the curved surface, measured from the edge at the top to a point on the circumference of the circle at the base, is known as the slant height of an object (such as a cone or pyramid). In other words, the slant height, represented either as s or l, is the shortest distance that may be traveled along the surface of the solid.

Slant height(l)=26cm

Radius(r)=10cm

It is known that, $l^{2}=r^{2}+h^{2}$