All categories

3 years ago

How to solve it and understand it

Mathematics

1 answer:

algol133 years ago

8 0

Volume of rectangle prism = w l h

Volume of rectangle pyramid = 1/3(w l h)

so Volume of rectangle pyramid = 1/3 (Volume of rectangle prism)

= 1/3 (240)

= 80

Answer:

80 cm^3

You might be interested in

Can someone help me with this please!

elena55 [62]

Answer:

Maybe 24 ft.......................????

7 0

3 years ago

Read 2 more answers

Please show the working and answer. you can take a picture for the working.

baherus [9]

Answer:

(a) The area of the triangle is approximately 39.0223 cm²

(b) ∠SQR is approximately 55.582°

Step-by-step explanation:

(a) By sin rule, we have;

SQ/(sin(∠SPQ)) = PQ/(sin(∠PSQ)), which gives;

5.4/(sin(52°)) = 6.8/(sin(∠PSQ))

∴ (sin(∠PSQ)) = (6.8/5.4) × (sin(52°)) ≈ 0.9923

∠PSQ = sin⁻¹(0.9923) ≈ 82.88976°

Similarly, we have;

5.4/(sin(52°)) = SP/(sin(180 - 52 - 82.88976))

Where, 180 - 52 - 82.88976 = ∠PQS = 45.11024

SP = 5.4/(sin(52°))×(sin(180 - 52 - 82.88976)) ≈ 4.8549

Given that RS : SP = 2 : 1, we have;

RS = 2 × SP = 2 × 4.8549 ≈ 9.7098

We have by cosine rule, $\overline {RQ}$ ² = $\overline {SQ}$ ² + $\overline {SR}$ ² - 2 × $\overline {SQ}$ × $\overline {SR}$ × cos(∠QSR)

∠QSR and ∠PSQ are supplementary angles, therefore;

∠QSR = 180° - ∠PSQ = 180° - 82.88976° = 97.11024°

∠QSR = 97.11024°

Therefore;

$\overline {RQ}$ ² = 5.4² + 9.7098² - 2 × 5.4×9.7098× cos(97.11024)

$\overline {RQ}$ ² ≈ 136.42

$\overline {RQ}$ = √(136.42) ≈ 11.6799

The area of the triangle = 1/2 × $\overline {PQ}$ × $\overline {PR}$ × sin(∠SPQ)

By substituting the values, we have;

1/2 × $\overline {PQ}$ × $\overline {PR}$ × sin(∠SPQ)

1/2 × 6.8 × (4.8549 + 9.7098) × sin(52°) ≈ 39.0223 cm²

The area of the triangle ≈ 39.0223 cm²

(b) By sin rule, we have;

$\overline {RS}$ /(sin(∠SQR)) = $\overline {RQ}$ /(sin(∠QSR))

By substituting, we have;

9.7098/(sin(∠SQR)) = 11.6799/(sin(97.11024))

sin(∠SQR) = 9.7098/(11.6799/(sin(97.11024))) ≈ 0.82493

∠SQR = sin⁻¹(0.82493) ≈ 55.582°.

8 0

3 years ago

An angle measures 67.2° less than the measure of a supplementary angle. What is the measure of each angle?

arlik [135]

Two supplementary angles always adds up to 180 degrees. If an angle is 67.2 degrees less than the measure of a supplementary angle, an equation can be formed where "A" represents the larger angle, and (A - 67.2) represents the smaller angle.

(A - 67.2)+A=180

(Combine the A's)

2A - 67.2=180

(Add 67.2 to both sides)

2A = 247.2

(Divide by 2 to both sides)

A = 123.6

123.6 degrees is the larger angle.

The smaller angle is represented by (A - 67.2). We now know the value of A so lets plug it in. (123.6 - 67.2) = 56.4. 56.4 is the value of the smaller angle.

We can double check to make sure we got the right answer.

123.6 + 56.4 = 180

4 0

3 years ago

Kristin is 20 km behind a truck that is driving 90 km/h how long will it take her to catch up to the truck? how far will she go

malfutka [58]

Time taken for Kristin to catch up with the truck will be found using the formula
time=(distance)/(speed)
distance=20 km
speed=90 km/h
thus
time=20/90=2/9 hours

Answer: 2/9 hours

5 0

3 years ago

Orlando has a loan with an effective interest rate of 7. 918%, compounded annually. Which of the following must be true? I. In t

svetlana [45]

The correct option is B, II. only.

Given to us,

I. In the effective rate formula, n is equal to one.

Effective interest rate formula,

$r = (1 + \dfrac{i}{n} )^n - 1.$

where,

r is the effective interest rate,

i is the stated interest rate,

n is the number of compounding periods per year.

According to the question the compounding periods per year is not given to us. Also, loans are taken for a longer period of time.

Thus, we can conclude that statement is false.

II. The nominal rate is 7. 918%.

nominal rate = real interest rate + inflation rate,

but as it is not mentioned in the question about the inflation rate. the statement is true to us. Assuming the inflation rate is 0%.

Thus, we can conclude that statement is true.

III. The Federal Funds Rate is static.

This statement is false, as the no information is given about this statement also this can not be concluded through assumption.

Thus, we can conclude that statement is false.

Hence, The correct option is B, II. only.

To know more visit:

brainly.com/question/15846526

4 0

3 years ago