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3 years ago

I need help with these two problems

Mathematics

1 answer:

erastova [34]3 years ago

5 0

Number 5 is 15.9 kilograms

And number 6 is 6 million cubic feet per minute

You just cross multiply

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The diagram shows a 9cm x 7cm rectangle-based pyramid. all the diagonal sides - TA, TB, TC, AND TD- are length 12cm. M is the mi

lakkis [162]

Answer:

∠TAC is approximately equal to 61.6°

Step-by-step explanation:

The given parameters for the pyramid are;

The dimension for the rectangular base are; Length = 9 cm, width = 7 cm

The length of the diagonal sides, TA, TB, TC, and TD = 12 cm each

The midpoint of the rectangular base = Point M

The diagonal AC = AM + MC

AM = MC as given M is the midpoint of the rectangular base

∴ AC = AM + MC = 2·AM

By Pythagoras' theorem, AC = √(9² + 7²) = √130

AC = √130 cm

∴ AM = AC/2 = (√130)/2 cm

Alternatively, AM = √((9/2 cm)² + (7/2 cm)²) = √(32.5) cm

∠TAC = ∠TAM

By trigonometric ratios, we have;

$cos (\theta) = \dfrac{Length \ of \ adjacent \ side \ to \ angle }{Length \ of \ hypotenuse\ side \ to \ angle}$

$\therefore cos (\angle TAM) = cos (\angle TAC) = \dfrac{\left (\dfrac{\sqrt{130} }{2} \right )}{12} = \dfrac{\sqrt{130} }{2 \times 12} = \dfrac{\sqrt{130} }{24}$

$\angle TAC = arccos \left ( \dfrac{\sqrt{130} }{24} \right ) \approx 61.6 ^{\circ} \ to 1 \ decimal \ place$

6 0

2 years ago

Can anyone help me with ratios

Elden [556K]

Well I am not good with ratios but I could try. What do you need help with?

5 0

3 years ago

X is inversely proportional to y, and x = 18 when y = 4. Write an equation relating the two

Alenkasestr [34]

Answer:

$xy=72$

Step-by-step explanation:

If x is inversely porportionaly to y, then for some constant k,

$x = \frac{k}{y}\\xy=k$

Since y is 4 when x = 18, k is equal to 4*18=72, so the equation is:

$xy=72$

8 0

3 years ago

If the mass of a material is 45 grams and the volume of the material is 11 cm^3, what would the density of the material be?

Nuetrik [128]

Answer:

Density of material would be 4.09 $g/cm^3$

units is $g/cm^3$

Step-by-step explanation:

Given: The mass of a material is 45 grams and the volume of the material is 11 cubic centimeter

Density is defined as mass per unit volume.

It is given by:

$p= \frac{m}{V}$ where p is the density , m is the mass and V is the volume of the material respectively.

Here, Density is expressed in grams per centimeter cubed (g/cubic cm)

Here, m = 45 g , V = 11 cubic cm

We get;

$p= \frac{45}{11}$ = 4.09 $g/cm^3$

therefore, density of a material would be, $4.09 g/cm^3$

and its units is $g/cm^3$

7 0

3 years ago

Divide 65 by 26 and write the answer as a mixed number

EleoNora [17]

2 1/2

65/26
26*2=52
65-52=13
13/26 = 1/2

5 0

3 years ago